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Question

Evaluate :
(vii) 2sin68cos222cot155tan753tan45tan20tan40tan50tan705

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Solution

We know,
cos(90θ)=sinθ
tan(90θ)=cotθ

cotθ=1tanθ

cos22=cos(9068)=sin68
tan75=tan(9015)=cot15
tan20=tan(9070)=cot70
tan40=tan(9050)=cot50

To evaluate,

2sin68cos222cot155tan753tan45tan20tan40tan50tan705

=2sin68sin682cot155cot153tan45cot70cot50tan50tan705

=2sin68sin682cot155cot153tan45tan50tan705tan70tan50

=22535

=2(2+3)5

=255

=21

=1

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